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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 11424.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11424.h1 | 11424q2 | \([0, -1, 0, -42432, -3350088]\) | \(16502300582616584/331494849\) | \(169725362688\) | \([2]\) | \(28672\) | \(1.2753\) | |
| 11424.h2 | 11424q3 | \([0, -1, 0, -11072, 401940]\) | \(293204888234504/35857918593\) | \(18359254319616\) | \([2]\) | \(28672\) | \(1.2753\) | |
| 11424.h3 | 11424q1 | \([0, -1, 0, -2742, -47880]\) | \(35637273157312/4552605729\) | \(291366766656\) | \([2, 2]\) | \(14336\) | \(0.92877\) | \(\Gamma_0(N)\)-optimal |
| 11424.h4 | 11424q4 | \([0, -1, 0, 4143, -255807]\) | \(1919569026752/7938130977\) | \(-32514584481792\) | \([4]\) | \(28672\) | \(1.2753\) |
Rank
sage: E.rank()
The elliptic curves in class 11424.h have rank \(0\).
Complex multiplication
The elliptic curves in class 11424.h do not have complex multiplication.Modular form 11424.2.a.h
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
